A note on numerical methods for mean-variance portfolio selection with dynamic attention behavior in a hidden Markov model

In this paper, we present some numerical methods for solving a mean-variance portfolio selection problem. Specifically, we study closed-loop equilibrium strategies for mean-variance portfolio selection problem in a hidden Markov model with the dynamic attention behavior. In addition to the investment strategy, the investor’s attention to news is introduced as a control of the accuracy of the news signal process. The main objective of this paper is to find equilibrium strategies by numerically solving an extended HJB equation using the classical Markov chain approximation method, the deep learning method, and the hybrid deep learning Markov chain approximation method. Finally, a numerical example is provided to compare the performance of the proposed three numerical methods.